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In-ABC-the-following-relationship-holds-golden-ratio-sinA-sinB-sinC-lt-1-1-2-




Question Number 151189 by mathdanisur last updated on 18/Aug/21
In  △ABC  the following relationship  holds: (𝛟-golden ratio)  sinA + ((sinB)/𝛟) + ((sinC)/𝛟) < (1/𝛟) + ((1+(√𝛟)+𝛟)/(2𝛟))
$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{the}\:\mathrm{following}\:\mathrm{relationship} \\ $$$$\mathrm{holds}:\:\left(\boldsymbol{\varphi}-\mathrm{golden}\:\mathrm{ratio}\right) \\ $$$$\mathrm{sinA}\:+\:\frac{\mathrm{sinB}}{\boldsymbol{\varphi}}\:+\:\frac{\mathrm{sinC}}{\boldsymbol{\varphi}}\:<\:\frac{\mathrm{1}}{\boldsymbol{\varphi}}\:+\:\frac{\mathrm{1}+\sqrt{\boldsymbol{\varphi}}+\boldsymbol{\varphi}}{\mathrm{2}\boldsymbol{\varphi}} \\ $$

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